The NEC covers appliance wiring as well. Stranded wire is usually more flexible than its solid counterpart. This is especially helpful when pulling it through conduit and when used as flexible cord. The type of insulation will have a big influence on the stiffness and overall diameter of the conductor.
It's been awhile but I believe (in part anyway) that appliance cord gets to be smaller than the circuit conductors because it is going to feed a dedicated load with a given, certain amount of load. (Think tap rule too). The one requirement I remember the NEC has is the cord has enough ampacity so that if it were to get damaged and the conductors short together, it could cause the breaker's instantaneous trip function to operate correctly. Take a lamp cord for example, it's much more likely for you to mash the cord (a short out the conductors and cause a short circuit than it is for you to load it up to twenty or more amps.
Got a reference for this?
Just noodling it - but you'd have to have really thin wire such that the resistance is high enough that it would not trip, roughly 8 ohms - something like 28 gauge wire (i.e. cat 5) for a ten foot stub that's shorted.
15 amps through 28 ga. .... yeah, that's not going to last long.
That said, I don't think I've seen many cords with 20 ga. or smaller.
Anyways, when sizing cables for widgets, the primary concern is going to be physical robustness and how much does it heat up when powered. That's what UL tests - attach a thermocouple, run the device at max ambient temp and ensure the cable doesn't exceed the rating.